An engineer designed a valve that will regulate water pressure on an automobile engine. the engineer designed the valve such that it would produce a mean pressure of 5.1 pounds/square inch. it is believed that the valve performs above the specifications. the valve was tested on 210 engines and the mean pressure was 5.2 pounds/square inch. assume the standard deviation is known to be 0.6. a level of significance of 0.1 will be used. determine the decision rule.

The critical region would be  

If we compare the p value and a significance level given we see that so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 5.1 pounds/square inch at 10% of significance.  

Step-by-step explanation:

Data given and notation  

represent the average score for the sample  

represent the population standard deviation  

sample size  

represent the value that we want to test  

represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to apply a one upper tailed test.  

What are H0 and Ha for this study?  

Null hypothesis:  

Alternative hypothesis :  

Compute the test statistic  

The statistic for this case is given by:  

(1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic  

We can replace in formula (1) the info given like this:  

Critical value

On this case since we have a right tailed test we need to look into the normal standard distribution and find a value that accumulates 0.1 of the area on the right of the distribution or 0.9 of the area on the left and for this case we see that

The critical region would be  

Give the appropriate conclusion for the test  

Since is a one side upper tailed test the p value would be:  

Conclusion  

If we compare the p value and a significance level given we see that so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 5.1 pounds/square inch at 10% of significance.  

step-by-step explanation: the declaration of the rights of man and of the citizen (french: déclaration des droits de l'homme et du citoyen de 1789), set by france's national constituent assembly in 1789, is a human civil rights document from the french revolution.[1]

the declaration was drafted by the abbé sieyès and the marquis de lafayette, in consultation with thomas jefferson.[2] influenced by the doctrine of "natural right", the rights of man are held to be universal: valid at all times and in every place, pertaining to human nature itself. it became the basis for a nation of free individuals protected equally by the law. it is included in the beginning of the constitutions of both the fourth french republic (1946) and fifth republic (1958) and is still current. inspired by the enlightenment philosophers, the declaration was a core statement of the values of the french revolution and had a major impact on the development of freedom and democracy in europe and worldwide.[3]

the 1789 declaration, together with the 1215 magna carta, the 1689 english bill of rights (1689), the 1776 united states declaration of independence, and the 1789 united states bill of rights, inspired in large part the 1948 united nations universal declaration of human rights

b. hoped i'm right lol

step-by-step explanation: